Forecasting Salmon Runs: A Time Series Analysis of Willamette Falls Fish Ladder Data

Willamette River Fish Bypass, Image by danny moore from Pixabay

Overview

The goal of this analysis is to visualize time series data of fish passage at the Willamette Falls fish ladder to identify trends, seasonal patterns, and annual variations in fish passage. Additionally, the analysis includes forecasting using the Holt-Winters method to predict future trends in salmon runs, providing critical information for watershed management and fish recovery efforts.

Background

Fish passage at Willamette Falls is critical for the survival of Oregon’s wild salmon and steelhead, which are on the brink of extinction due to dams blocking access to spawning habitats and degrading river ecosystems. With populations at just 1–2% of their historic levels, this analysis helps uncover migration trends and forecast future passage, providing valuable insights to guide recovery efforts, improve watershed management, and ensure these iconic species are protected for future generations.

Data Summary

This project explores adult fish passage data recorded at the Willamette Falls fish ladder on the Willamett River, Oregon from 2001 to 2010. The dataset provides valuable insights into the migration patterns of five salmon species: Chinook, Jack Chinook, Steelhead, Coho, and Jack Coho.

Data Citation: U.S. Army Corps of Engineers, NWD, et al. DART Adult Passage Counts Daily for All Species. Data accessed via Columbia River DART (Data Access in Real Time) on January 25, 2023.

Analysis Outline

1. Exploratory Data Analysis
2. Data Preprocessing
3. Visualization of Time Series
4. Visualization of Seasonplots for each species
5. Plot Annual Totals for Fish Passage
6. Apply Holt-Winters Forecasting
7. Summarize Trends and Patterns

Set Up

The following libraries will be used for data manipulation, visualization, and building regression models.

library(tidyverse)
library(here)
library(lubridate)
library(tsibble)
library(feasts)
library(fable)
library(kableExtra)
library(patchwork)
library(skimr)

Import data, replace NA values with zero, convert Date column from character to data and convert df to tsibble using the as_tsibble() function.

# Import data
fish_df <- read_csv(here('data', 'willamette_fish_passage.csv')) %>% 
  #replace(is.na(.),0) %>% 
  janitor::clean_names()

# Convert to ts
fish_ts <- fish_df %>% 
  mutate(date = mdy(date)) %>% 
  as_tsibble(key = NULL,
             index = date) %>% 
  replace(is.na(.), 0)

Preliminary Data Exploration

The original dataset contains multiple empty columns with over 3,000 missing values. Therefore, this study focuses on three salmon species—Coho, Jack Coho, and Steelhead salmon—for further analysis.

Click here to expand summary table

skim(fish_df)

Data summary

Name	fish_df
Number of rows	3652
Number of columns	16
_______________________
Column type frequency:
character	2
logical	8
numeric	6
________________________
Group variables	None

Variable type: character

skim_variable	n_missing	complete_rate	min	max	empty	n_unique	whitespace
project	0	1	16	16	0	1	0
date	0	1	6	8	0	3652	0

Variable type: logical

skim_variable	n_missing	complete_rate	mean	count
chinook_run	3652	0	NaN	:
wild_steelhead	3652	0	NaN	:
sockeye	3652	0	NaN	:
shad	3652	0	NaN	:
lamprey	3652	0	NaN	:
bull_trout	3652	0	NaN	:
chum	3652	0	NaN	:
pink	3652	0	NaN	:

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
chinook	1543	0.58	250.48	476.52	1.0	7.00	35.0	236.00	3883.0	▇▁▁▁▁
jack_chinook	2433	0.33	11.22	16.37	1.0	2.00	6.0	14.00	170.0	▇▁▁▁▁
steelhead	203	0.94	85.97	115.68	-2.0	8.00	28.0	127.00	709.0	▇▂▁▁▁
coho	2694	0.26	76.03	160.84	-2.0	3.25	15.0	57.75	1290.0	▇▁▁▁▁
jack_coho	2971	0.19	21.03	37.02	1.0	2.00	7.0	22.00	380.0	▇▁▁▁▁
temp_c	1382	0.62	12.94	6.04	0.6	7.80	11.7	17.80	26.7	▂▇▆▃▃

Decomposition Summary

To better understand the structure of time series data, it’s useful to decompose to separately explore contributions of the different components (trend, seasonality, etc). This study employs Seasonal and Trend Decomposition using LOESS (Locally Estimated Scatterplot Smoothing), a method for estimating nonlinear relationships. It applies a weighted moving average across all points in the dataset, with weights determined by their distance from the point being averaged. STL() function from the feasts is used to obtain decomposition.

Click here to expand decomposition plots

Jack Coho

# Prepare data for plotting
fish_long <- fish_ts %>% 
  select('date', 'steelhead','coho', 'jack_coho') %>% 
  pivot_longer(
    cols = -date,
    names_to = "species",
    values_to = "counts"
  )

# Obtain decomposition
jack_dcmp <- fish_long %>% 
  filter(species =='jack_coho') %>% 
  model(STL(counts~season(period = "1 year") + trend(window = 25)))

# Visualize components
components(jack_dcmp) %>% 
  autoplot()+
  theme_classic()

Coho Salmon

# Obtain decomposition
coho_dcmp <- fish_long %>% 
  filter(species =='coho') %>% 
  model(STL(counts~season(period = "1 year") + trend(window = 25)))

# Visualize components
components(coho_dcmp) %>% 
  autoplot()+
  theme_classic()

Steelhead

# Obtain decomposition
jack_dcmp <- fish_long %>% 
  filter(species =='steelhead') %>% 
  model(STL(counts~season(period = "1 year") + trend(window = 25)))

# Visualize components
components(jack_dcmp) %>% 
  autoplot()+
  theme_classic()

Data Visualization

Daily Time Series Plot

# Create plot
ggplot(fish_long, aes(x=date, y=counts, color=species)) +
  geom_line() +
  labs(title = "Time Series Plots of Salmon Adult Passage",
       x = "Time",
       y = "Counts") +
  scale_color_brewer(palette = "Set2")+
  theme_minimal()+
  facet_wrap(~species,ncol=1)+
  theme(legend.position='none')

Figure 1: Time Series of Adult Passage for Coho, Jack Coho, and Steelhead salmon.

From the time series plots in Figure 1, we can observe the following observations:

• Steelhead consistently has higher counts compare to Coho and Jack Coho salmon. There is relatively low abundance of Jack Coho salmon, with smaller and less frequent peaks compared to the other species.
• All three species exhibit seasonal peaks in their counts. Steelhead salmon displays broader and more frequent peaks over time, suggesting a longer migration period.
• There is increasing trend in the counts of Coho salmon after 2008, with higher peaks observed in subsequent years.

Seasonplots

A seasonplot can help point out seasonal patterns, and help to glean insights over the years. We’ll use feasts::gg_season() to create an exploratory seasonplot, which has month on the x-axis, salmon counts on the y-axis, and each year is its own series (mapped by line color).

fish_long %>% 
  gg_season(y=counts, pal=hcl.colors(n=10)) + 
  theme_light()+
  labs(title='Seasonplots of Daily Counts for Salmon Passage by Species',
    x="month",
       y="Species Counts")

Figure 2: Seasonplots of Daily Counts for Salmon Passage by Species

Figure 2 displays the seasonal variation in the counts of salmon species across all years, with each line representing a specific year and highlighting recurring monthly patterns. Since the daily counts were too stochastic and busy, especially for steelhead salmon, I opted to use monthly means for clearer interpretation.

Seasonplots with monthly means:

fish_month <- fish_long %>% 
  index_by(yr_mo = ~yearmonth(.)) %>% 
  group_by(species) %>% 
  summarize(month_mean = mean(counts, na.rm=TRUE)) %>% 
  ungroup()

#fish_month
fish_month %>% 
  gg_season(y=month_mean, pal=hcl.colors(n=10)) + 
  theme_light()+
  labs(title='Seasonplots of Monthly Average Counts for Salmon Passage by Species',
       x="month",
       y="Species Counts")

Figure 3: Seasonplots of Monthly Average Counts for Salmon Passage by Species

Figure 2 and 3 shows the monthly variation in counts for three salmon species across multiple years:

• Both Coho and Jack Coho salmon show a sharp and well-defined seasonal peak in September, with Coho consistently having significantly higher peak counts compared to Jack Coho, as also seen in the original time series.
• Steelhead salmon exhibit a broader seasonal pattern, with counts steadily increasing from January to a peak in May or June, followed by a rapid decline, suggesting a longer migration period.
• Interannual variability is noticeable, particularly in Coho, where a sharper increase in counts is observed in later years.

Annual Counts

# Prep data for plotting
fish_yr <- fish_long %>% 
  index_by(year = ~year(.)) %>%
  group_by(species) %>% 
  summarize(annual_total = sum(counts)) %>% 
  ungroup()
# Convert year column to factor
fish_yr$year = as.factor(fish_yr$year)

fish_yr %>%
  ggplot(aes(x = year, y = annual_total, color = species, group = species)) +  # Explicitly group by species
  geom_line() +
  theme_minimal() +
  labs(
    title = "Annual Total Counts of Fish Passage by Species",
    x = "Year",
    y = "Counts"
  ) +
  scale_color_brewer(palette = 'Set2')

Figure 4: Plot of Annual Counts of Fish Passage by Species

• Annual Steelhead counts show significant interannual variability, with drop of 25000 counts between 2002 and 2003.
• Jack Coho salmon consistently has the lowest counts among the three species, with minimal variation over the years.
• Coho counts remain relatively low until 2008, after which there’s a sharp increas, reaching a significant peak with annual counts over 25,000 in 2010.

Forecast

We use the ETS() function from the fable package to generate predictions. Exponential smoothing calculates weighted averages of past observations, with the weights decreasing exponentially as the observations become older. Given the change in variance over time, we specify multiplicative seasonality, and set restrict as FALSE to allow function to find best model.

The results show negative counts for Steelhead and Jack Coho salmon, which is unrealistic and indicates that this forecasting method is not suitable for salmon data.

salmon_ts <- fish_ts %>% select(date, coho, jack_coho, steelhead)

# Reshape the data into a long format
salmon_long <- salmon_ts %>%
  pivot_longer(cols = c(coho, jack_coho, steelhead), 
               names_to = "species", 
               values_to = "counts")

# Fit the ETS model for each species

ets_models <- salmon_long %>%
  model(ets = ETS(counts~season("M"), restrict=FALSE))

# Generate forecasts for each species 
forecasts <- ets_models %>%
  forecast(h = "5 years")

# Plot the forecasts along with historical data
forecasts %>%
  autoplot(salmon_long, level = NULL) +
  labs(
    title = "Historical and Forecasted Salmon Passage by Species",
    y = "Counts",
    x = "Date"
  ) +
  theme_minimal()

kable(ets_models, col.names=c("Species","ETS Model(Error, Trend, Seasonality)"), caption = "ETS Models by Species")

ETS Models by Species

Species	ETS Model(Error, Trend, Seasonality)
coho
jack_coho	<ETS(A,N,M)>
steelhead	<ETS(A,N,M)>

The differences in the ETS models arise because the ETS() function automatically selects the best model based on the data for each species. For Jack Coho and Steelhead, the data likely exhibited clear seasonal patterns with varying magnitudes, leading to the selection of a model with multiplicative seasonality. In contrast, Coho data may not show significant seasonal or trend components, so no model were selected.

Summary

Forecast results suggest that forcing a seasonal model may not be appropriate. Further exploration is needed to find the correct model for forecasting. Here we use a autocorrelation function to confirm our interpretation.

Autocorrelation function (ACF) shows how correlated observations within a series are with pervious observations on the same variable. In the context of salmon passage, the ACF helps identify patterns in the monthly average counts of steelhead salmon passing through the ladder over time. This analysis is useful for guiding selection of models to forecast future values in a time series.

Click here to expand ACF plots

Steelhead

For Steelhead salmon, I do not expect exponential smoothing (ETS) to be the most effective forecasting method due to its broader and more variable seasonal pattern and significant interannual variability.

# autocorrelation for steelhead
fish_month %>% 
  filter(species == 'steelhead') %>% 
  ACF(month_mean) %>% 
  autoplot() +
  theme_minimal()+
  labs(
    title="ACF plot for Steelhead Salmon Passage",
    x="lag (in month)",
    y="autocorrelation coefficient"
  )

Coho

For Coho salmon, I do not expect exponential smoothing (ETS) to be the most effective forecasting method due to its broader and more variable seasonal pattern and significant interannual variability.

# autocorrelation for steelhead
fish_month %>% 
  filter(species == 'coho') %>% 
  ACF(month_mean) %>% 
  autoplot() +
  theme_minimal()+
  labs(
    title="ACF plot for Steelhead Salmon Passage",
    x="lag (in month)",
    y="autocorrelation coefficient"
  )

Jack Coho

# autocorrelation for steelhead
fish_month %>% 
  filter(species == 'jack_coho') %>% 
  ACF(month_mean) %>% 
  autoplot() +
  theme_minimal()+
  labs(
    title="ACF plot for Steelhead Salmon Passage",
    x="lag (in month)",
    y="autocorrelation coefficient"
  )

For Jack Coho salmon, the highest correlation coefficient occurs at lags of 12 months, indicating seasonality. This suggests that exponential smoothing could be a suitable forecasting method.